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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationFri, 06 May 2011 16:48:28 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/06/t1304700272z0lixpl6sw4u3yr.htm/, Retrieved Mon, 13 May 2024 03:42:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121169, Retrieved Mon, 13 May 2024 03:42:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact103

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [] [2011-05-06 16:48:28] [cd3c8dd726b701571412eb3280c696e7] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
814
1150
1225
1691
1759
1754
2100
2062
2012
1897
1964
2186
966
1549
1538
1612
2078
2137
2907
2249
1883
1739
1828
1868
1138
1430
1809
1763
2200
2067
2503
2141
2103
1972
2181
2344
970
1199
1718
1683
2025
2051
2439
2353
2230
1852
2147
2286
1007
1665
1642
1518
1831
2207
2822
2393
2306
1785
2047
2171
1212
1335
2011
1860
1954
2152
2835
2224
2182
1992
2389
2724
891
1247
2017
2257
2255
2255
3057
3330
1896
2096
2374
2535
1041
1728
2201
2455
2204
2660
3670
2665
2639
2226
2586
2684
1185
1749
2459
2618
2585
3310
3923

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121169&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121169&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121169&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ www.wessa.org






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11717.83333333333431.5797268246741372
21862.83333333333471.8522174913621941
31970.91666666667384.9808633575381365
41912.75456.2623099211081469
51949.5476.8278706009311815
62072.5476.8381658001341623
72184.16666666667668.686070294622439
82396.58333333333627.6030097751192629

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1717.83333333333 & 431.579726824674 & 1372 \tabularnewline
2 & 1862.83333333333 & 471.852217491362 & 1941 \tabularnewline
3 & 1970.91666666667 & 384.980863357538 & 1365 \tabularnewline
4 & 1912.75 & 456.262309921108 & 1469 \tabularnewline
5 & 1949.5 & 476.827870600931 & 1815 \tabularnewline
6 & 2072.5 & 476.838165800134 & 1623 \tabularnewline
7 & 2184.16666666667 & 668.68607029462 & 2439 \tabularnewline
8 & 2396.58333333333 & 627.603009775119 & 2629 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121169&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]1717.83333333333[/C][C]431.579726824674[/C][C]1372[/C][/ROW]
[ROW][C]2[/C][C]1862.83333333333[/C][C]471.852217491362[/C][C]1941[/C][/ROW]
[ROW][C]3[/C][C]1970.91666666667[/C][C]384.980863357538[/C][C]1365[/C][/ROW]
[ROW][C]4[/C][C]1912.75[/C][C]456.262309921108[/C][C]1469[/C][/ROW]
[ROW][C]5[/C][C]1949.5[/C][C]476.827870600931[/C][C]1815[/C][/ROW]
[ROW][C]6[/C][C]2072.5[/C][C]476.838165800134[/C][C]1623[/C][/ROW]
[ROW][C]7[/C][C]2184.16666666667[/C][C]668.68607029462[/C][C]2439[/C][/ROW]
[ROW][C]8[/C][C]2396.58333333333[/C][C]627.603009775119[/C][C]2629[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121169&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121169&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11717.83333333333431.5797268246741372
21862.83333333333471.8522174913621941
31970.91666666667384.9808633575381365
41912.75456.2623099211081469
51949.5476.8278706009311815
62072.5476.8381658001341623
72184.16666666667668.686070294622439
82396.58333333333627.6030097751192629






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-234.323453836731
beta0.365294543072597
S.D.0.11839582235442
T-STAT3.08536682974404
p-value0.0215148646935115

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -234.323453836731 \tabularnewline
beta & 0.365294543072597 \tabularnewline
S.D. & 0.11839582235442 \tabularnewline
T-STAT & 3.08536682974404 \tabularnewline
p-value & 0.0215148646935115 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121169&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-234.323453836731[/C][/ROW]
[ROW][C]beta[/C][C]0.365294543072597[/C][/ROW]
[ROW][C]S.D.[/C][C]0.11839582235442[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.08536682974404[/C][/ROW]
[ROW][C]p-value[/C][C]0.0215148646935115[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121169&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121169&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-234.323453836731
beta0.365294543072597
S.D.0.11839582235442
T-STAT3.08536682974404
p-value0.0215148646935115






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.30751651765246
beta1.38218326040691
S.D.0.481099515363158
T-STAT2.87296747610226
p-value0.0283169413707981
Lambda-0.382183260406912

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.30751651765246 \tabularnewline
beta & 1.38218326040691 \tabularnewline
S.D. & 0.481099515363158 \tabularnewline
T-STAT & 2.87296747610226 \tabularnewline
p-value & 0.0283169413707981 \tabularnewline
Lambda & -0.382183260406912 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121169&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.30751651765246[/C][/ROW]
[ROW][C]beta[/C][C]1.38218326040691[/C][/ROW]
[ROW][C]S.D.[/C][C]0.481099515363158[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.87296747610226[/C][/ROW]
[ROW][C]p-value[/C][C]0.0283169413707981[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.382183260406912[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121169&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121169&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.30751651765246
beta1.38218326040691
S.D.0.481099515363158
T-STAT2.87296747610226
p-value0.0283169413707981
Lambda-0.382183260406912


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
(n <- length(x))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')